The results of the design study of an advanced scheme for the 14-MeV intense neutron source based on muon-catalyzed fusion (CF) are presented. A pion production target (liquid lithium) and a synthesizer [liquid deuterium-tritium (D-T) mixture] are considered. Negative pions are produced inside a 17/7 T magnetic field by an intense (2-GeV,12-mA) deuteron beam interacting with the 150-cm-long, 0.75-cm-radius lithium target. Muons from the pion decay are collected in the backward direction and stopped in the D-T mixture of the synthesizer. The synthesizer has the shape of a 10-cm-radius sphere surrounded by two 0.03-cm-thick titanium shells. At 100 CF events/muon, it can produce up to 1017n/s of 14-MeV neutrons. A quasi-isotropic neutron flux up to 1014 n/cm2s-1 can be achieved in the test volume of ~2.5 l with an irradiated surface of ~350 cm2. The thermophysical and thermomechanical analyses show that the technological limits are not exceeded.